High-resolution soft X-ray spectroscopy of the prototype accretion disk wind quasar, PDS 456, is presented. Here, the XMM-Newton reflection grating spectrometer spectra are analyzed from the large 2013–2014 XMM-Newton campaign, consisting of five observations of approximately 100 ks in length. During the last observation (OBS. E), the quasar is at a minimum flux level, and broad absorption line (BAL) profiles are revealed in the soft X-ray band, with typical velocity widths of σᵥ ~ 10,000 km s⁻¹. During a period of higher flux in the third and fourth observations (OBS. C and D, respectively), a very broad absorption trough is also present above 1 keV. From fitting the absorption lines with models of photoionized absorption spectra, the inferred outflow velocities lie in the range ~0.1-0.2c. The absorption lines likely originate from He and H-like neon and L-shell iron at these energies. A comparison with earlier archival data of PDS 456 also reveals a similar absorption structure near 1 keV in a 40 ks observation in 2001, and generally the absorption lines appear most apparent when the spectrum is more absorbed overall. The presence of the soft X-ray BALs is also independently confirmed by an analysis of the XMM-Newton EPIC spectra below 2 keV. We suggest that the soft X-ray absorption profiles could be associated with a lower ionization and possibly clumpy phase of the accretion disk wind, where the latter is known to be present in this quasar from its well-studied iron K absorption profile and where the wind velocity reaches a typical value of 0.3c.